Problem: Multiply the following complex numbers: $({-2+i}) \cdot ({-1-5i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-2+i}) \cdot ({-1-5i}) = $ $ ({-2} \cdot {-1}) + ({-2} \cdot {-5}i) + ({1}i \cdot {-1}) + ({1}i \cdot {-5}i) $ Then simplify the terms: $ (2) + (10i) + (-1i) + (-5 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 2 + (10 - 1)i - 5i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 2 + (10 - 1)i - (-5) $ The result is simplified: $ (2 + 5) + (9i) = 7+9i $